1. ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Lecture 33
Power System Stabilizers (PSS)
Professor M.A. Pai
Department of Electrical and Computer Engineering
© 2000 University of Illinois Board of Trustees, All Rights Reserved

2. Functions of a PSS
PSS adds a signal to the excitation system proportional to speed deviation. This adds positive damping.
Signal is generated locally from the shaft.
Both local mode and inter-area mode can be damped. When oscillation is observed on a system or a planning study reveals poorly damped oscillations, use of participation factors helps in identifying the machine(s) where PSS has to be located.
Tuning of PSS regularly is important.
Modal Analysis technique forms the basis for multi-machine systems.

3. Basic Approach DAE Model
Linearizing about an operating point
PSS principles are best understood for a single machine infinite bus (SMIB) system.

4. SMIB System (Flux Decay Model)
Flux Decay Model and Fast Exciter ~
How are computed for a multi-machine system?

5. Computation of Suppose at generator i we wish to obtain
Consider rest of the machines as infinite buses with voltages fixed.
From the physical terminal of generator i, obtain a Thevenin equivalent (i.e. short circuit all other generators and do network reduction) to get
This can be repeated for all other generators to get the SMIB equivalents.

6. Stator Equations
Assume Stator Algebraic Equations are:

7. Network Equations
The network equation is (assuming zero phase angle at the infinite bus and no local load)
Simplifying, ~

8. Complete SMIB Model
Machine
Stator equations
Network equations ~

9. Linearization of SMIB Model

10. Linearization (contd)
Final Steps involve
Linearizing Machine Equations
Substitute (1) in the linearized equations of (2).

11. Linearization of Machine Equations
Symbolically we have
Substitute (3) in (2) to get linearized model.

12. Linearized SMIB Model Excitation system is yet to be included.
K1 – K4 constants are:

13. K1 – K6 Constants
K1 – K4 only involve machine and not the exciter.

14. Computing Before linearizing exciter equations, compute
is an algebraic variable in the Excitation System.

15. Computing While linearizing stator algebraic equations, we had
Substitute this in expression for to get
We thus have K1 – K6 constant.
Next construct the Heffron – Philips model.

16. Heffron – Phillips Model
Add a fast exciter
Linearize
This together with
Gives
SMIB Model

17. Block Diagram
K1 – K6 affected by system loading and

18. Numerical Example
Initial conditions ~

19. Initial Conditions (contd)
From the stator algebraic equation,

20. Initial Conditions (contd)
From non linear model, setting derivatives = 0,
This completes the calculation of the initial conditions.

21. Computation of K1 – K6 Constants
The formulas are used.

22. Effect of Field Flux on System Stability
With constant field voltage, ,from block diagram
are usually positive.
For low frequencies and in steady state,
Field flux variation due
to feedback.(Armature
reaction) introduces
negative synchronizing
torque.

23. Effect of Field Flux At higher frequencies This is a phase with
Hence results in a positive damping component.
In general, positive damping torque and negative synchronizing
torque due to at typical oscillation frequencies (1-3 Hz).

24. Effect of Field Flux There are situations when can become negative.
Case1. A hydraulic generator without damper winding, light load ( is small) and connected to a line with high ratio and large system.
Case 2. Machine is connected to a large local load, supplied partly by generator and partly by remote large system.
If , damping due to is negative

25. Effect of Excitation System
Ignore dynamics of
Gain through is
If , then gain becomes positive.
Large enough K5 may make system unstable

26. Numerical Example (Effect of )
Test system 1 Test System 2
Eigen Values
Test System Test System 2
unstable